TLDR – 20 companies in a VC portfolio is the optimal balance between risk and reward, offering a very high chance of hitting outsized returns without significant risk of losing money. This is exactly the approach we follow at Two Small Fish Ventures, as we keep our per-fund portfolio size limited to roughly 20 companies.

In my previous post, VC is a Home Run Derby with Uncapped Runs, I illustrated mathematically why early-stage venture funds’ success doesn’t hinge on minimizing failures, nor does it come from hitting singles (e.g., the number of “3x” companies). These smaller so-called “wins” are just noise.

As I said:

“Venture funds live or die by one thing: the percentage of the portfolio that becomes breakout successes — those capable of generating returns of 10x, 100x, or even 1000x.”

To drive high expected returns for VCs, finding these breakout successes is key. However, expected value alone doesn’t tell the full story. We also need to consider variance. In simple terms, even if a fund’s expected return is 5x or 10x, it doesn’t necessarily mean it’s a good investment. If the variance is too high—meaning the fund has a low probability of achieving that return and a high probability of losing money—it would still be a poor bet.

For example, imagine an investment opportunity that has a 10% chance of returning 100x and a 90% chance of losing everything. Its expected return is 10x (i.e., 10% x 100x + 90% x 0x = 10x). But despite the attractive expected return, it’s still a terrible investment due to the extremely high risk of total loss.

That said, there’s a time-tested solution to turn this kind of high-risk investment into a great one: diversification. While everyone understands the importance of diversification, the real key lies in how it’s done. By building a properly diversified portfolio, we can reduce variance while maintaining a high expected return. This post will illustrate mathematically how the right portfolio construction allows venture funds to generate outsized returns while ensuring a high probability of success.

Moonshot Capital vs. PlayItSafe Capital: A Quick Recap

Let’s start by revisiting our two hypothetical venture capital firms: Moonshot Capital and PlayItSafe Capital. Moonshot Capital swings for the fences, aiming to find the next 100x company while expecting most of the portfolio to fail. PlayItSafe Capital, on the other hand, protects downside risk (at least that’s what they think), but by avoiding bigger risks, it sacrifices the chance of finding outsized returns.

• Moonshot Capital: Out of 20 companies, 17 resulted in strikeouts (0x returns), 3 companies achieved 10x returns, and 1 company achieved a 100x return.

• PlayItSafe Capital: Out of 20 companies, 7 resulted in strikeouts (0x returns), 7 companies broke even (1x), 5 companies achieved 3x returns, and 1 company achieved a 10x return.

Here’s how their expected returns compare:

• Moonshot Capital has an expected return of 6.5x, thanks to one company yielding 100x and three companies yielding 10x (i.e. (1 x 100 + 3 x 10 +16 x 0) x $1 = $130).

• PlayItSafe Capital has a much lower expected return of 1.6x, with its highest return from one 10x company, five 3x returns, and several breakeven companies (i.e. (1 x 10 + 5 x 3 + 7 x 1 + 7 x 0) x $1 = $32).

Despite these differences in expected returns, what’s surprising is that counterintuitively, the probability of losing money (i.e., achieving an average return of less than 1x at the fund level) is quite similar for both firms.

Let’s dive into the math to see how we calculate these probabilities:

Moonshot Capital: 12.9% Probability of Losing Money

1. Expected Return :

2. Variance :

3. Standard Deviation :

4. Standard Error :

Using a normal approximation, the z-score to calculate P(X < 1) is:

Looking this up in the standard normal distribution table gives us:

P(X < 1) = 0.129 or 12.9%

PlayItSafe Capital: 11.6% Probability of Losing Money

Similarly, looking this up in the standard normal distribution table gives us (sparing you all the equations):

P(X < 1) = 0.116 or 11.6%

Shockingly, these two firms’ probabilities of losing money are essentially the same. The math does not lie!

Here’s a graphical representation of the outcomes (probability density) for Moonshot Capital and PlayItSafe Capital.

Probability Density Graphs: Comparing Moonshot and PlayItSafe

As you can see, Moonshot has higher upside potential, as the density peaks at 6x, while PlayItSafe is more concentrated around lower returns. Since their downside risks are more or less the same while PlayItSafe’s approach significantly limits its upside, counterintuitively PlayItSafe is far riskier from the risk-reward perspective.

Proper Portfolio Construction: How Portfolio Size Affects Returns

To further optimize Moonshot’s strategy, we will explore how different portfolio sizes affect the balance between risk and reward. Below, I’ve analyzed the outcomes (i.e. portfolio size sensitivity) for Moonshot Capital across portfolio sizes of n = 5, n = 10, n = 20, and n = 30.

The graph below shows the probability density curves for Moonshot Capital with varying portfolio sizes:

As you can see, smaller portfolios (n = 5, n = 10) exhibit higher variance, with a greater spread of potential outcomes. Larger portfolios (n = 20, n = 30) reduce the variance but also diminish the likelihood of hitting outsized returns.

Why 20 is the Optimal Portfolio Size

1. Why 20 is Optimal:

At n = 20, Moonshot Capital strikes an ideal balance. The risk of losing money, i.e. P (X < 1), remains manageable at 12.9%, while the probability of outsized returns remains high: 62.1% chance of hitting a return higher than 5x. This suggests that Moonshot’s high-risk, high-reward approach pays off without exposing the fund to unnecessary risk.

2. Why Bigger Isn’t Always Better (n = 30):

When the portfolio size increases to n = 30, we see a significant drop-off in the likelihood of outsized returns. The probability of achieving a return higher than 5x drops significantly from 62.1% at n = 20 to 41.9% at n = 30, and counterintuitively, the risk of losing money starts to increase. This suggests that larger portfolios can dilute the impact of the big wins that drive fund returns. It also mathematically explains why “spray-and-pray” does not work for early-stage investments.

3. The Pitfalls of Small Portfolios (n = 5 and n = 10):

At smaller portfolio sizes, such as n = 5 or n = 10, the variance increases significantly, making the portfolio’s returns more unpredictable. For example, at n = 5, the probability of losing money is significantly higher, and the risk of extreme outcomes becomes more pronounced. At n = 10, the flat-curve suggests that the variance is very high. This high variance means the returns are volatile and difficult to predict, increasing risk.

Conclusion: How to Win the Home Run Derby With Uncapped Runs

The key takeaway here is that Moonshot Capital’s strategy of swinging for the fences doesn’t mean taking on excessive risk. With 20 companies in the portfolio, Moonshot is the optimal between risk and reward, offering a very high chance of hitting outsized returns without significant risk of losing money.

While n=20 is optimal, n=10 is also pretty good, but n=30 is significantly worse. So, a ‘concentrated’ approach – but not ‘n=5 concentrated’ – is far better than ‘spray and pray,’ if you have to pick between the two.

This is exactly the approach we follow at Two Small Fish Ventures. We don’t write a cheque unless we have that magical “100x conviction.” We also keep our per-fund portfolio size limited to roughly 20 companies. This blog post mathematically breaks down one of our many secret sauces for our success.

Don’t tell anyone.

P.S. This blog is licensed under a Creative Commons Attribution 4.0 International License. You are free to copy, redistribute, remix, transform, and build upon the material for any purpose, even commercially, as long as appropriate credit is given.